Question

on march 24, 1989, the exxon valdez oil tanker ran aground and leaked millions of gallons of oil into prince william sound. the spill covered approximately 11,000 square miles of ocean. the oil spread out in a circular pattern and the radius increased by 0.10 mph. use $pi = 3.14$. at this rate, how many hours did it take for oil to cover the area? 187 hours 592 hours 1,871 hours 5,917 hours

Explanation:

Step1: Recall the area formula for a circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. We know $A = 11000$ square - miles and $\pi=3.14$. We need to find $r$.

Step2: Solve for the radius $r$

From $A=\pi r^{2}$, we can rewrite it as $r^{2}=\frac{A}{\pi}$. Substitute $A = 11000$ and $\pi = 3.14$ into the formula: $r^{2}=\frac{11000}{3.14}\approx3503.185$. Then $r=\sqrt{3503.185}\approx59.2$ miles.

Step3: Calculate the time $t$

We know the rate of change of the radius is $v = 0.10$ mph. Using the formula $v=\frac{r}{t}$, we can solve for $t$. Rearranging the formula gives $t=\frac{r}{v}$. Substitute $r\approx59.2$ miles and $v = 0.10$ mph into the formula: $t=\frac{59.2}{0.10}=592$ hours.

Answer:

592 hours